Expressing various facial emotions is an important social ability for efficient communication between humans. A key challenge in human-robot interaction research is providing androids with the ability to make various human-like facial expressions for efficient communication with humans. The android Nikola, we have developed, is equipped with many actuators for facial muscle control. While this enables Nikola to simulate various human expressions, it also complicates identification of the optimal parameters for producing desired expressions. Here, we propose a novel method that automatically optimizes the facial expressions of our android. We use a machine vision algorithm to evaluate the magnitudes of seven basic emotions, and employ the Bayesian Optimization algorithm to identify the parameters that produce the most convincing facial expressions. Evaluations by naïve human participants demonstrate that our method improves the rated strength of the android's facial expressions of anger, disgust, sadness, and surprise compared with the previous method that relied on Ekman's theory and parameter adjustments by a human expert.